Analyticity and continuation of certain functions of two complex variables
Author:
Carl H. Fitzgerald
Journal:
Proc. Amer. Math. Soc. 25 (1970), 536-540
MSC:
Primary 32.35
DOI:
https://doi.org/10.1090/S0002-9939-1970-0261034-4
MathSciNet review:
0261034
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper shows that the satisfaction of a certain quadratic relation is a sufficient condition that a continuous, symmetric function of two complex variables on a domain be analytic and be continuable to a particular larger domain. This quadratic relation is of the same type as that involved in the Grunsky inequalities.
- Ju. E. Alenicyn, Univalent functions without common values in a multiply connected domain, Trudy Mat. Inst. Steklov. 94 (1968), 4–18 (Russian). MR 0225989
- Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439
- S. Bergman and M. Schiffer, Kernel functions and conformal mapping, Compositio Math. 8 (1951), 205–249. MR 39812
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Additional Information
Keywords:
Grunsky inequalities,
Bergman kernel function,
analytic continuation,
two complex variables,
doubly orthogonal functions
Article copyright:
© Copyright 1970
American Mathematical Society